Question

Find the equivalent resistance of the given circuit and hence find the current

flowing through the circuit. ​

Answer 1

Answer:

The equivalent resistance of the given circuit is 12 Ω

The current flowing through the circuit is 2 A

Explanation:

To know :  

• When resistors of resistances R₁ , R₂ , R₃ .... are connected in series, the equivalent resistance (R) is given by

R = R₁ + R₂ + R₃ + ...  

• When resistors of resistances R₁ , R₂ , R₃ .... are connected in parallel, the equivalent resistance (R) is given by

1/R = 1/R₁ + 1/R₂ + 1/R₃ + ...

In the given circuit,

R₃ and R₄ are connected in series.

Let R₃₄ be the equivalent resistance of this series combination.

R₃₄ = R₃ + R₄

R₃₄ = 6 Ω + 4 Ω

R₃₄ = 10 Ω

R₃₄ and R₂ are in parallel combination.

Let R₂₃₄ be it's equivalent resistance

1/R₂₃₄ = 1/R₃₄ + 1/R₂

1/R₂₃₄ = 1/10 + 1/10

1/R₂₃₄ = 2/10

1/R₂₃₄ = 1/5

R₂₃₄ = 5 Ω

R₂₃₄ and R₁ are connected in series.

Let R₁₂₃₄ be it's equivalent resistance.

R₁₂₃₄ = R₂₃₄ + R₁

R₁₂₃₄ = 5 Ω + 7 Ω

R₁₂₃₄ = 12 Ω

Therefore, the equivalent resistance of the given circuit is 12 Ω

From Ohm’s Law Equation :

V = IR

where

V denotes the voltage

I denotes the current

R denotes the resistance

 

Given, the voltage across the circuit is 24 V  

Substituting the values,  

24 = I × 12  

I = 24/12  

I = 2 A  

∴ The current flowing through the circuit is 2 A